Consider a Sonar system with range resolution AR = 4cm.

(a) A sinu- soidal pulse at frequency fo = 100KHz is transmitted. What is the pulse width, and what is the bandwidth?

(b) By using an up-chirp LFM, centered at fo, one can increase the pulse width for the same range resolution. If you want to increase the transmitted energy by a factor of 20, give an expression for the transmitted pulse.

(c) Give an expression for the causal filter matched to the LFM pulse in part b.